The matching law

Abstract

This article introduces the quantitative analysis of choice behavior by describing a number of equations developed over the years to describe the relation between the allocation of behavior under concurrent schedules of reinforcement and the consequences received for alternative responses. Direct proportionality between rate of responding and rate of reinforcement was observed in early studies, suggesting that behavioral output matched environmental input in a mathematical sense. This relation is termed "strict matching," and the equation that describes it is referred to as "the matching law." Later data showed systematic departures from strict matching, and a generalized version of the matching equation is now used to describe such data. This equation, referred to as "the generalized matching equation," also describes data that follow strict matching. It has become convention to refer to either of these equations as "the matching law." Empirical support for the matching law is briefly summarized, as is the applied and practical significance of matching analyses.